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Convergence of Continued Fractions

Published online by Cambridge University Press:  20 November 2018

William B. Jones  and
W. J. Thron
William B. Jones
Affiliation:
University of Colorado, Boulder, Colorado
W. J. Thron
Affiliation:
University of Colorado, Boulder, Colorado
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Let {sn(z)} be a given sequence of linear fractional transformations (or simply l.f.t.'s) of the form

1.1

and let

1.2

The sequence of l.f.t.'s {Sn(z)} is called a continued fraction generating sequence (or simply a c.f.g. sequence).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1037 - 1055
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Hillam, K. L. and Thron, W. J., A general convergence criterion for continued fractions K(an/bn), Proc. Amer. Math. Soc. 16 (1965), 1256–1262.Google Scholar
2. Jones, William B. and Thron, W. J., Further properties of T-fractionst Math. Ann. 166 (1966), 106–118.Google Scholar
3. Perron, Oskar, Die Lehre von den Kettenbriichen, 3rd éd., Vol. 2 (Teubner, Verlagsgesellschaft, Stuttgart, 1957).Google Scholar
4. Thron, W. J., Convergence regions for the general continued fraction, Bull. Amer. Math. Soc. 49 (1943), 913–916.Google Scholar
5. Thron, W. J., Some properties of continued fractions 1 + d0z + K(z/(1 + dnz)), Bull. Amer. Math. Soc. 54 (1948), 206–218.Google Scholar
6. Thron, W. J., Convergence of sequences of linear fractional transformations and of continued fractions, J. Indian Math. Soc. 27 (1963), 103–127.Google Scholar
7. Wall, H. S., Analytic theory of continued fractions (Van Nostrand, Princeton, N.J., 1948).Google Scholar